1. Field of the Invention
The invention relates to a X-ray imaging method, in which a body to be examined (3) is received by a support (1) and in which,                a X-ray (i, j) beam (7) is emitted from a focal point (F1,F2) of a source (5) towards the body (3),        an intensity is attenuated due to the passage of the X-rays through the body and detected by a detector (9) irradiated by the beam, for different pairs of angular positions (θa,θb) taken by the body or the source (5)—detector (9) assembly around a rotation axis (Ω), said two angular positions (θa,θb) of said different pairs having an angular difference (Δ),        the detected intensities are converted into data (c(a),ρ(b)) by a digital converter (11) and,        the data (c(a),ρ(b)) are processed by a programmed computer (13) using the following formula:        
  C  =                    ρ                  (          b          )                    n        +                  c                  (          a          )                    n        -                  1                  2          n          2                    ⁢              (                                            ∑                              k                =                1                            n                        ⁢                          c              k                              (                a                )                                              +                                    ∑                              u                =                1                            n                        ⁢                          ρ              u                              (                b                )                                                    )            
to calculate a value (C) of the attenuation coefficient at a point (P0) of a set of points {P0}, for a given pair of said angular positions (θa,θb), in order to obtain an image representing an X-ray attenuation coefficient for said set of points {P0} of the body (3), where, in the formula:
c(a) is the data coming from the intensity detected at an impact point T(a) of a first ray i passing through said point P0 for said first angular position θa,
ρ(b) is the data coming from the intensity detected at an impact point R(b) of a second ray j passing through said point P0 for said second angular position θb,
      ∑          k      =      1        n    ⁢      c    k          (      a      )      is the load associated with said first ray impact point T(a), defined by the sum of data ck(a) coming from intensities detected in the first angular position θa, along n points Tk(a) of a first load calculation line passing closest to said first impact point T(a), and
      ∑          u      =      1        n    ⁢      ρ    u          (      b      )      is the load associated with said second ray impact point R(b), defined by the sum of data ρu(b) coming from the intensities detected in the second angular position θb, along n points Ru(b) of a second load calculation line passing closest to said second impact point R(b).
2. Description of Related Art
A process of this type is known from French patent application FR 2,888,374 and international patent application WO 2007/006560 filed by the inventor. The attenuation coefficient C at point P0 is calculated by the so-called direct generation method. The calculation only requires the c(a) and ρ(b) data coming from the intensities detected at two impact points of the two X-rays passing through said point P0 for the first and the second angular positions taken by the body or the source—detector assembly around the rotation axis Ω.
The direct generation formula described in patent applications FR 2,888,374 and WO 2007/006560 derives from a simplification of the general formula of the Lagrangian:
      C    ij    =            B      ij        +                  1        n            ⁢              (                              ρ            j                    -                                    ∑                              i                =                1                            n                        ⁢                          B              ij                                      )              +                  1        m            ⁢              (                              c            i                    -                                    ∑                              j                =                1                            m                        ⁢                          B              ij                                      )              -                  1        nm            ⁢              (                                            ∑                              j                =                1                            m                        ⁢                          ρ              j                                -                                    ∑                              i                =                1                            n                        ⁢                                          ∑                                  j                  =                  1                                m                            ⁢                              B                ij                                                    )            wherein Bij is equated with the half sum of the detected intensity ci at said first impact point, divided by the number m of impact points of said first load line and the detected intensity ρj at said second impact point, divided by the number n of impact points of the second load line:
      B    ij    =            1      2        ⁢          (                                    ρ            j                    n                +                              c            i                    m                    )      
and wherein, due to conservation of the total irradiation dose:
            ∑              i        =        1            n        ⁢          c      i        =            ∑              j        =        1            m        ⁢          ρ      j      
As a result:
      C    ij    =                    ρ        j            n        +                  c        i            m        -                  1                  2          ⁢                                          ⁢          nm                    ⁢              (                                            ∑                              i                =                1                            n                        ⁢                          c              i                                +                                    ∑                              j                =                1                            m                        ⁢                          ρ              j                                      )            
The special case where n=m leads to:
      C    ij    =                    ρ        j            n        +                  c        i            n        -                  1                  2          n          2                    ⁢                        ∑                      k            =            1                    n                ⁢                  (                                    ρ              k                        +                          c              k                                )                    
The direct generation method is used to calculate the attenuation coefficient of a set of points {P0} belonging to a sectional plane of the body, perpendicularly to the rotation axis Ω. Under these conditions, the loads associated with the first and second impact points are calculated along two load calculation lines defined by the trace of the sectional plane on the detector, for the first and second angular positions taken by the body or the source—detector assembly around the rotation axis Ω. The value of the associated loads is constant for all P0 points belonging to the sectional plane.
The basic operations for calculating the attenuation coefficient C lead to a very significant time saving. The subtractive term that accounts for loads associated with the first and second impact points is calculated once for all and its value is only called in the calculation of the attenuation coefficient C of all points P0 of the sectional plane. In addition, the calculation of the attenuation coefficient C does not require back-projection of the image obtained in the first angular position into the image obtained in the second angular position. Direct calculation from the data c(a) and ρ(b) coming from the intensities detected at two impact points leads to a significant reduction in calculation errors.
However, the calculation of the attenuation coefficient C in a sectional plane perpendicular to the rotation axis Ω requires to move the body or the source—detector assembly parallel to said axis, to obtain images of a series of sectional planes, ie to explore a volume of the body to be examined.